Mix the crushed chocolate cookies with the melted butter in a medium-sized bowl until well coated. Press this mixture into the base of a 9-inch springform pan to create a solid crust. Refrigerate for about 10 minutes to set.
In a large bowl, beat the softened cream cheese with an electric mixer until silky smooth. Gradually add the confectioners' sugar and vanilla extract, blending until fully combined.
In another bowl, whip the heavy cream until stiff peaks form. Carefully fold the whipped cream into the cream cheese mixture, keeping it light and airy.
Gently drizzle the melted chocolate into the cream cheese mixture, folding until fully blended and creamy.
Transfer the chocolate filling onto the chilled crust, smoothing the surface with a spatula.
Cover the springform pan with plastic wrap and refrigerate for a minimum of 4 hours, preferably overnight.
When ready to serve, adorn the top with chocolate curls or cocoa powder, release the sides of the springform pan, and cut into slices to enjoy.